The propagation of waves of acoustic frequencies in curved ducts is studied for the first four modes. The analysis makes use of Bessel functions to construct curves of wave number in the duct versus imposed wave number. The results apply to ducts of arbitrary width and arbitrary radii of curvature. The characteristics of motion in a bend are compared with propagation of waves in a straight duct, and important differences in the behavior of waves are noted.

Topics: NASA Technical Reports Server (NTRS), ACOUSTIC DUCTS, ACOUSTIC FREQUENCIES, CURVATURE, SOUND WAVES,...

A linear combination of modified Bessel functions is defined, discussed briefly, and tabulated. This combination was found to recur in the analysis of various heat transfer problems and in the analysis of the thermal behavior of living tissue when modeled by cylindrical shells.

Topics: NASA Technical Reports Server (NTRS), BESSEL FUNCTIONS, HEAT TRANSFER, THERMAL DIFFUSION, ANALYSIS...

The various plate integrals previously considered by Crighton (1972) are directly recast in a manner that permits their systematic development near the source point; and thus to dispense with manipulation of the velocity transform. The advantage is the ease with which distributed forces over the plate are incorporated into the analysis. After the procedure is introduced in connection with a line source problem and followed by consideration of a point source, the analogous problems relative to...

Topics: NASA Technical Reports Server (NTRS), ASYMPTOTIC SERIES, BESSEL FUNCTIONS, FORCED VIBRATION,...

The integral expression for the mutual admittance between circular apertures in a planar array is evaluated in closed form. Very good accuracy is realized when compared with values that were obtained by numerical integration. Utilization of this closed-form expression, for all element pairs that are separated by more than one element spacing, yields extremely accurate results and significantly reduces the computation time that is required to analyze the performance of a large electronically...

Topics: NASA Technical Reports Server (NTRS), ANTENNA ARRAYS, APERTURES, ELECTROMAGNETIC COUPLING, PHASED...

This volume was digitized and made accessible online due to deterioration of the original print copy.

Topics: Bessel functions, Boundary value problems.

The construction of a theoretical flow field due to shedding of vortex rings, the identification of the controlling parameters, and the determination of whether the theoretical model successfully simulated the unsteady pressure field near jet (and consequently the far field noise) was studied. The basic parameters contained in the analytic solutions were the epoch at which a vortex ring was shed near the jet exit and the eddy viscosity coefficient. These parameters were identified from the...

Topics: NASA Technical Reports Server (NTRS), JET AIRCRAFT NOISE, JET FLOW, MATHEMATICAL MODELS,...

An automated mass spectrometer analysis system is disclosed, in which samples are automatically processed in a sample processor and converted into volatilizable samples, or their characteristic volatilizable derivatives. Each volatilizable sample is sequentially volatilized and analyzed in a double focusing mass spectrometer, whose output is in the form of separate ion beams all of which are simultaneously focused in a focal plane. Each ion beam is indicative of a different sample component or...

Topics: NASA Technical Reports Server (NTRS), MASS SPECTROMETERS, SPECTRAL RESOLUTION, BESSEL FUNCTIONS,...

190
190

Oct 22, 2012
10/12

by
Berry, L. A. (Leslie A.)

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Sound radiation generated by mechanical or vibratory source arrangements and, in some instances of planar or piston types, encompasses all magnitudes of the wavelength or frequency as well as disposition of the observation site. The comparative increase in average total radiated power from infinitesimally small or point sources of periodic strength, on passing from rest to steady rectilinear motion, depends only on Mach number in the noncompact case; and a formally analogous rise in output is...

Topics: NASA Technical Reports Server (NTRS), FLUID FLOW, PISTONS, SOUND PROPAGATION, VIBRATION,...

The solution of the one dimensional, time independent, Schroedinger equation in which the energy minus the potential varies as the nth power of the distance is obtained from proper linear combinations of Bessel functions. The linear combinations called generalized Airy functions, reduce to the usual Airy functions Ai(x) and Bi(x) when n equals 1 and have the same type of simple asymptotic behavior. Expressions for the generalized Airy functions which can be evaluated by the method of...

Topics: NASA Technical Reports Server (NTRS), AIRY FUNCTION, QUANTUM MECHANICS, SCHROEDINGER EQUATION,...

An overview of a normal mode method of solving the Helmholtz wave equation to describe the underwater sound field for a fixed point source in a plane multilayered medium is presented. The mode functions are well-defined at all depths of the medium as they are continuous across turning points of the separated depth-dependent differential equation. Comparisons of model results to a limited number of benchmark propagation solutions are presented.

Topics: DTIC Archive, NAVAL UNDERSEA WARFARE CENTER DIV NEWPORT RI, *WAVE PROPAGATION, *HELMHOLTZ...

The M-ary character error probability, Pe, for a communications system employing D-fold diversity combination is derived and evaluated for the case of no fading, over the range of parameters M = 2, 3, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and D = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64 for Pe in the range .1 to .00001. The curves presented allow for ready determination of the additional signal-to-noise ratio required for employing diversity when it is not necessary, or when uncertainty forces...

Topics: DTIC Archive, Nuttall,Albert H, NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB,...

Properties of the space charge waves in a solid relativistic electron beam propagating in a cylindrical waveguide is investigated, including the important influence of arbitrary wall impedance. The stability analysis is carried out within the framework of the linearized Vlasov-Maxwell equations. In order to examine the influence of the axial momentum spread on the stability behavior, it is assumed that all electrons have a Lorentzian distribution in the axial canonical momentum. One of the most...

Topics: DTIC Archive, Uhm,Han S, NAVAL SURFACE WEAPONS CENTER SILVER SPRING MD, *ELECTROMAGNETIC WAVE...

The power output from given sources is usually ascertained via an energy flux integral over the normal directions to a remote (far field) surface; an alternative procedure, which utilizes an integral that specifies the direct rate of working by the source on the resultant field, is described and illustrated for both point and continuous source distribution. A comparison between the respective procedures is made in the analysis of sound radiated from a periodic dipole source whose axis performs...

Topics: NASA Technical Reports Server (NTRS), ACOUSTICS, DIPOLE MOMENTS, POINT SOURCES, RADIANT FLUX...

Properties of the space charge waves in a solid relativistic electron beam propagating in a cylindrical waveguide is investigated, including the important influence of arbitrary wall impedance. The stability analysis is carried out within the framework of the linearized Vlasov-Maxwell equations. In order to examine the influence of the axial momentum spread on the stability behavior, it is assumed that all electrons have a Lorentzian distribution in the axial canonical momentum. One of the most...

Topics: DTIC Archive, Uhm,Han S, NAVAL SURFACE WEAPONS CENTER SILVER SPRING MD, *ELECTROMAGNETIC WAVE...

Properties of the space charge waves in a solid relativistic electron beam propagating in a cylindrical waveguide is investigated, including the important influence of arbitrary wall impedance. The stability analysis is carried out within the framework of the linearized Vlasov-Maxwell equations. In order to examine the influence of the axial momentum spread on the stability behavior, it is assumed that all electrons have a Lorentzian distribution in the axial canonical momentum. One of the most...

Topics: DTIC Archive, Uhm,Han S, NAVAL SURFACE WEAPONS CENTER SILVER SPRING MD, *ELECTROMAGNETIC WAVE...

Present solution for the electromagnetic scattering by a vertex are either approximate or difficult to use for computations. For example, GTD solutions for vertex scattering are not yet fully developed and yield approximate results of unknown accuracy. The exact eigenfunction solution is both difficult to use and computationally inefficient due to the large number of eigenfunctions that must be retained. In this work, we obtain the scattering by a vertex (e.g., a quarter plane) by employing the...

Topics: DTIC Archive, Sahalos,J N, OHIO STATE UNIV COLUMBUS ELECTROSCIENCE LAB, *EIGENVECTORS,...

These tables are intended as an aid in the calculation of axisymmetric wave motion in cylindrical structures using elastic, viscoelastic and viscous materials. They have been calculated by straightforward summing of the power and asymptotic series. The programs can be used to print more extensive tables, should the demand exist.

Topics: DTIC Archive, Lindemann, O, GOULD INC GLEN BURNIE MD CHESAPEAKE INSTRUMENT DIV, *TABLES(DATA),...

An improved method for computation of phase functions has been implemented in computer code AGAUS to obtain more reliable results for large diameter particles under conditions of relatively high absorption. The new routine uses a partial backward recursion and the method of continued fractions. This represents an improvement over the forward recursion method. A brief outline of the later method is given for review and comparison. Results are presented which show that the new routine is reliable...

Topics: DTIC Archive, Burlbaw,Edward, NEW MEXICO STATE UNIV LAS CRUCES DEPT OF PHYSICS, *COMPUTERIZED...

Approximations to some generalized functions generated by the process of differentiation are developed and used to interpret some integrals involving generalized functions. Application to the realization of the ideal voltage response pattern of an array is made and illustrated for both an impulsive and a smooth approximation to the required generalized weighting function.

Topics: DTIC Archive, Nuttall,Albert H, NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB,...

A computer program is described and listed. This program calculates electromagnetic penetration of a TM plane wave into the cylindrical cavity for which rho or = a when the surface (rho = a, phi sub O n = phi or = 2 pi - rho sub O) is perfectly conducting. Here, rho and phi are cylindrical coordinates. The z directed electric field E sub z in the slot aperture (rho = a, - phi sub or = phi n = phi sub O) is expressed as a linear combination of 4 even and 4 odd expansion functions. The method of...

Topics: DTIC Archive, Mautz,Joseph R, SYRACUSE UNIV NY DEPT OF ELECTRICAL AND COMPUTER ENGINEERING,...

In this work, we discuss the solution of the differential equations in the cylindrical coordinate system for the case of a coupled CE reaction mechanism at a finite disk electrode. We use the properties of discontinuous integrals of Bessel functions to treat the mixed boundary conditions at the electrode surface and the surrounding insulator. The results are compared to previous analyses and we also make comparisons of various estimates of the chronoamperometric response for constant surface...

Topics: DTIC Archive, Pons, Stanley, UTAH UNIV SALT LAKE CITY DEPT OF CHEMISTRY, *CHEMICAL REACTIONS,...

Present solution for the electromagnetic scattering by a vertex are either approximate or difficult to use for computations. For example, GTD solutions for vertex scattering are not yet fully developed and yield approximate results of unknown accuracy. The exact eigenfunction solution is both difficult to use and computationally inefficient due to the large number of eigenfunctions that must be retained. In this work, we obtain the scattering by a vertex (e.g., a quarter plane) by employing the...

Topics: DTIC Archive, Sahalos,J N, OHIO STATE UNIV COLUMBUS ELECTROSCIENCE LAB, *EIGENVECTORS,...

A unified approach is applied to the derivation of a number of formulas for the probability of signal detection and the probability of false alarm. The context is incoherent integration, with fluctuating signal-to-noise ratios and/or fluctuating thresholds. The standard results are obtained and extended to more general fluctuation models. A fundamental duality is established between fluctuating signals and fluctuating thresholds and used to simplify the derivations. Also included is an...

Topics: DTIC Archive, Kelly, Edward J, MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB, *SIGNAL...

The free-free transition is studied for an electron-hydrogen atom in ground state when a low-energy electron (external) is injected into hydrogenic plasma in the presence of an external homogenous, monochromatic, and linearly polarized laser field. The effect of plasma screening is considered in the Debye-Huckel approximation. The calculations are performed in the soft photon limit. The incident electron is considered to be dressed by the laser field in a nonperturbative manner by choosing the...

Topics: NASA Technical Reports Server (NTRS), ATOMIC ENERGY LEVELS, DENSE PLASMAS, ELECTRON ENERGY, PLASMAS...

2
2.0

May 18, 2021
05/21

by
Onoe, Morio

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338 pages 28 cm

Topics: Bessel functions -- Tables, Mathématiques, Tables mathématiques, Bessel functions

These tables are intended as an aid in the calculation of axisymmetric wave motion in cylindrical structures using elastic, viscoelastic and viscous materials. They have been calculated by straightforward summing of the power and asymptotic series. The programs can be used to print more extensive tables, should the demand exist.

Topics: DTIC Archive, Lindemann, O, GOULD INC GLEN BURNIE MD CHESAPEAKE INSTRUMENT DIV, *TABLES(DATA),...

The spatial eigenvalue expansion procedure which we have used previously to study viscous flow in rotating and nutating cylinders is studied in the high Reynolds number limit. It is shown that in this limit there is a significant simplification in the procedure used to determine the amplitudes of the eigenfunctions used to describe the forced velocity field in the cylinder. More precisely, it is shown that these amplitudes can, to the order of Reynolds number used in this paper, be simply...

Topics: DTIC Archive, Hall, Philip, ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD, *LIQUID FILLED...

195
195

May 30, 2011
05/11

by
Nelson, Karl W.; McArthur, Crai

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This presentation reviews the activities of the Advanced Space Transportation Program (ASTP) in the development of Rocket-Based Combined Cycle (RBCC)technology. The document consist of the presentation slides for a talk scheduled to be given to the World Aviation Congress and Exhibit of SAE. Included in the review is discussion of recent accomplishments in the area of Advanced Reusable technologies (ART), which includes work in flowpath testing, and system studies of the various vehicle/engine...

Topics: DISPLACEMENT MEASUREMENT, ELECTRO-OPTICS, HOLOGRAPHY, MODULATION, BESSEL FUNCTIONS, DIFFRACTION...

The development of an analytical model to estimate the shielding of one jet by an adjacent jet in a twin jet configuration is discussed in relation to aircraft generated noise. The azimuthal redistribution of sound defining the shadow zone is investigated. Wave equations were solved in the plane normal to the jet axis to estimate the diffraction and reflection of sound by a heated, cylindrical jet. Thus, the noise source considered is essentially a line source assumed to emit at discrete...

Topics: NASA Technical Reports Server (NTRS), ACOUSTIC MEASUREMENT, AIRCRAFT MODELS, ENGINE NOISE, JET...

Using methods associated with Zernicke's polynomial expansion, we discussed atmospheric dispersion effects in dual wavelength adaptive optics systems. On the basis of dual frequency correlations associated with phase expansion coefficients, we solved for residual phase errors produced by atmospheric dispersion. The results clearly showed that, although atmospheric dispersion will cause phase compensation to be imperfect, the use, however, of light sources with wavelengths even shorter than the...

Topics: DTIC Archive, Feng, Yuezhong, NATIONAL AIR INTELLIGENCE CENTER WRIGHT-PATTERSON AFB OH, *ADAPTIVE...

The M-ary character error probability, Pe, for a communications system employing D-fold diversity combination is derived and evaluated for the case of no fading, over the range of parameters M = 2, 3, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and D = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64 for Pe in the range .1 to .00001. The curves presented allow for ready determination of the additional signal-to-noise ratio required for employing diversity when it is not necessary, or when uncertainty forces...

Topics: DTIC Archive, Nuttall,Albert H, NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB,...

Properties of the space charge waves in a solid relativistic electron beam propagating in a cylindrical waveguide is investigated, including the important influence of arbitrary wall impedance. The stability analysis is carried out within the framework of the linearized Vlasov-Maxwell equations. In order to examine the influence of the axial momentum spread on the stability behavior, it is assumed that all electrons have a Lorentzian distribution in the axial canonical momentum. One of the most...

Topics: DTIC Archive, Uhm,Han S, NAVAL SURFACE WEAPONS CENTER SILVER SPRING MD, *ELECTROMAGNETIC WAVE...

Present solution for the electromagnetic scattering by a vertex are either approximate or difficult to use for computations. For example, GTD solutions for vertex scattering are not yet fully developed and yield approximate results of unknown accuracy. The exact eigenfunction solution is both difficult to use and computationally inefficient due to the large number of eigenfunctions that must be retained. In this work, we obtain the scattering by a vertex (e.g., a quarter plane) by employing the...

Topics: DTIC Archive, Sahalos,J N, OHIO STATE UNIV COLUMBUS ELECTROSCIENCE LAB, *EIGENVECTORS,...

Present solution for the electromagnetic scattering by a vertex are either approximate or difficult to use for computations. For example, GTD solutions for vertex scattering are not yet fully developed and yield approximate results of unknown accuracy. The exact eigenfunction solution is both difficult to use and computationally inefficient due to the large number of eigenfunctions that must be retained. In this work, we obtain the scattering by a vertex (e.g., a quarter plane) by employing the...

Topics: DTIC Archive, Sahalos,J N, OHIO STATE UNIV COLUMBUS ELECTROSCIENCE LAB, *EIGENVECTORS,...

The M-ary character error probability, Pe, for a communications system employing D-fold diversity combination is derived and evaluated for the case of no fading, over the range of parameters M = 2, 3, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and D = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64 for Pe in the range .1 to .00001. The curves presented allow for ready determination of the additional signal-to-noise ratio required for employing diversity when it is not necessary, or when uncertainty forces...

Topics: DTIC Archive, Nuttall,Albert H, NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB,...

Previous attempts to derive the homogeneous closed form solution to the problem of the dynamic motion of a zero bending rigidity cylinder in a viscous stream have expressed the solution as an infinite series involving Bessel functions of complex argument and order, which are often impractical to evaluate because of their complexity. Moreover, when these solutions are extended to nonhomogeneous situations, a harmonic time dependence is assumed that requires forcing the system by an arbitrary...

Topics: DTIC Archive, Lee,Ding, NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB, *CYLINDRICAL...

Properties of the space charge waves in a solid relativistic electron beam propagating in a cylindrical waveguide is investigated, including the important influence of arbitrary wall impedance. The stability analysis is carried out within the framework of the linearized Vlasov-Maxwell equations. In order to examine the influence of the axial momentum spread on the stability behavior, it is assumed that all electrons have a Lorentzian distribution in the axial canonical momentum. One of the most...

Topics: DTIC Archive, Uhm,Han S, NAVAL SURFACE WEAPONS CENTER SILVER SPRING MD, *ELECTROMAGNETIC WAVE...

This note describes how to use Brent's multiple-precision arithmetic package newly made available for the ASC. This note also enumerates some of the concomitant mathematical functions, constants and software. In addition, a comparison of computation times for the basic arithmetic operations is made between this package and the existing ASC multiple-precision arithmetic software. (Author)

Topics: DTIC Archive, Miller,A R, NAVAL RESEARCH LAB WASHINGTON DC, *COMPUTER PROGRAM DOCUMENTATION,...

This note describes how to use Brent's multiple-precision arithmetic package newly made available for the ASC. This note also enumerates some of the concomitant mathematical functions, constants and software. In addition, a comparison of computation times for the basic arithmetic operations is made between this package and the existing ASC multiple-precision arithmetic software. (Author)

Topics: DTIC Archive, Miller,A R, NAVAL RESEARCH LAB WASHINGTON DC, *COMPUTER PROGRAM DOCUMENTATION,...

This note describes how to use Brent's multiple-precision arithmetic package newly made available for the ASC. This note also enumerates some of the concomitant mathematical functions, constants and software. In addition, a comparison of computation times for the basic arithmetic operations is made between this package and the existing ASC multiple-precision arithmetic software. (Author)

Topics: DTIC Archive, Miller,A R, NAVAL RESEARCH LAB WASHINGTON DC, *COMPUTER PROGRAM DOCUMENTATION,...

An improved method for computation of phase functions has been implemented in computer code AGAUS to obtain more reliable results for large diameter particles under conditions of relatively high absorption. The new routine uses a partial backward recursion and the method of continued fractions. This represents an improvement over the forward recursion method. A brief outline of the later method is given for review and comparison. Results are presented which show that the new routine is reliable...

Topics: DTIC Archive, Burlbaw,Edward, NEW MEXICO STATE UNIV LAS CRUCES DEPT OF PHYSICS, *COMPUTERIZED...

An improved method for computation of phase functions has been implemented in computer code AGAUS to obtain more reliable results for large diameter particles under conditions of relatively high absorption. The new routine uses a partial backward recursion and the method of continued fractions. This represents an improvement over the forward recursion method. A brief outline of the later method is given for review and comparison. Results are presented which show that the new routine is reliable...

Topics: DTIC Archive, Burlbaw,Edward, NEW MEXICO STATE UNIV LAS CRUCES DEPT OF PHYSICS, *COMPUTERIZED...

The problem of electromagnetic transmission through a slab where transmitting and receiving antennas are at finite distances from the slab is of concern. The mathematical formulation of the problem is quite general. A detailed solution is presented for the case of a highly conducting slap exposed to sinusoidal and transient excitations. A discussion is given of the conditions under which measurements with source and receiver at finite distances are equivalent to the same measurements with plane...

Topics: DTIC Archive, Franceschetti,G, CALIFORNIA INST OF TECH PASADENA, *ELECTROMAGNETIC WAVE PROPAGATION,...

An automated program for reducing data from holographic reconstructions of particle fields is described. The instrumentation is based on the optical measurements of the Quantimet-720 Image Analyzing Computer. The focal plane detection of individual images is particularly emphasized by theoretical derivations and by experimental results.

Topics: DTIC Archive, Menzel, R W, ARNOLD ENGINEERING DEVELOPMENT CENTER ARNOLD AFB TN, *COMPUTER...

We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.

Topics: NASA Technical Reports Server (NTRS), BESSEL FUNCTIONS, EIGENVALUES, EIGENVECTORS, NONLINEARITY,...

The Final Proceedings for 20th Century Harmonic Analysis 2 July 2000 - 15 July 2000 published as Vol. 33 of NATO Science Series II. Mathematics, Physics and Chemistry Topics include pure and applied harmonic analysis.

Topics: DTIC Archive, Byrnes, James S, CAMBRIDGE UNIV (UNITED KINGDOM), *HARMONIC ANALYSIS, ALGORITHMS,...

A new technique of generating spherical Bessel functions of real or complex argument is developed. A negative simple continued fraction is defined and error corrections developed for the calculation of the continued fraction. FORTRAN IV programs for spherical Bessel functions of real and complex argument are presented. The technique is simple, test, and of higher accuracy than comparable techniques currently in use to evaluate spherical Bessel functions. (Author)

Topics: DTIC Archive, Lentz,W J, ARMY ELECTRONICS RESEARCH AND DEVELOPMENT COMMAND WSMR NM ATMOSPHERIC...

Document describes a LISP library of mathematical functions which calculates hyperbolic and inverse hyperbolic functions, Bessel functions, elliptic integrals, the gamma and beta functions, and the incomplete gamma abd beta functions. There are probability density functions, cumulative distributions, and random number generators for the normal, Poisson, chi-square, Student's T and Snedecor's F functions. Multiple linear regression, Fletcher-Powell unconstrained minimization, numerical...

Topics: DTIC Archive, Roylance,G, MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB,...

The M-ary character error probability, Pe, for a communications system employing D-fold diversity combination is derived and evaluated for the case of no fading, over the range of parameters M = 2, 3, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and D = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64 for Pe in the range .1 to .00001. The curves presented allow for ready determination of the additional signal-to-noise ratio required for employing diversity when it is not necessary, or when uncertainty forces...

Topics: DTIC Archive, Nuttall,Albert H, NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB,...